Saving textures and materials
I think this question is about misunderstanding. Maybe someone doesnt know what your talking about or maybe you don't understand how to ask the question right? In either case......
If you save image to HDD, it will be saved. ..done. There is no reason why Blender should be  deleting them. 

But:
If you bake, paint, texture, or edit an image in Blender, then you must save them  before you close the project. Blender will don't save images when you save .blend file.